State Estimation And Filtering Of Several Types Genetic Regulatory Networks With Mixed Time Delays

It is well known that the process of gene expression from genes to proteins is mainly composed of gene transcription and mRNA translation.The mechanisms of regulating the gene expression are called the genetic regulatory networks(GRNs).GRNs have attracted widespread attention in the field of biological and biomedical sciences,through the regulation of gene expression,microbes can be effectively synthesized beneficial bacteria for medical treatment.Therefore,the study of the GRNs has a very important practical significance.Due to the slow processes of transcription,translation and translocation,time-delay is inevitable in the GRNs,and parameter fluctuation caused by the modeling process as well as external disturbance caused by the environmental changes all make the system complicated,which lead to the fact that the states of the GRNs are difficult to obtain.In general,the states of the system needs to be estimated using available measurement data.However,when the computer measures network information,an important issue is the discretization of continuous systems,i.e.,sampling,that is,the information the computer measured is actually discrete sampling data.Therefore,the purpose of this paper is to study the state estimation for several types GRNs with mixed time-delay through the available discrete sampling data,and to design state estimator and recursive filter to estimate the concentrations of states mRNAs and proteins.The main contributions of this work can be listed as follows:Firstly,the state estimation problem of uncertain GRNs with time-delays is investigated.For GRNs with time-varying delays and uncertain parameters,the measurable output is constructed via using sampled data,and the robust state estimator based on measurable output is designed,on the basis of Lyapunov method,the sufficient conditions that guarantee the globally robustly asymptotic stability of the original system and the error system are derived by utilizing the Jensen inequality and the lower bound theorem,and then the design methods of estimator gain matrices are given.For GRNs subject to random delays,uncertain parameters and external disturbances,the robust H? state estimator based on measurable data is similarly constructed,by employing Lyapunov method,the sufficient conditions are deduced to guarantee that the augmented system is globally robustly asymptotically stable in the mean-square sense and satisfies H? performance by means of the lower bound theorem and the free-weighting matrix method,and then the specific expression forms of the required estimator gain matrices are presented.Some mumerical examples are shown to illustrate the validity and feasibility of the state estimators.Secondly,the filtering problem of delayed GRNs is studied.For discrete-time GRNs with state delay and random one-step measurement delay,by exploiting the state augmentation approach and the Riccati equation method,the recursive filter is designed,then the filtering error covariance matrix is calculated and its upper bound is estimated,the filter gain matrix of minimizing the upper bound is obtained according to the method of completing squares.Moreover,the filtering performance is analyzed with regard to the boundedness of the filtering error,the sufficient condition is derived to ensure that the filtering error is exponentially bounded in the mean-square sense.A numerical example is used to verify the effectiveness of the proposed filter.